The 25-year-old star returned to Chelsea in the new year following a loan stint in Germany at Fortuna Dusseldorf.
According to Turkish outlet FutbolArena, they have agreed to take Baker on loan from the Premier League heavyweights.
The deal between the two sides will see the Black Sea Storm hold an option to make the move permanent at the end of the star’s loan contract.
While Trabzonspor could land Baker on a permanent basis, it remains to be seen what sum has been agreed between the two parties.
Trabzonspor will be the Englishman’s eighth loan team, having already enjoyed stints at Sheffield Wednesday, MK Dons, Reading, Middlesbrough, Leeds, Vitesse and Dusseldorf.
The Turkish club are currently being managed by ex-Chelsea star Eddie Newton and Lewis will look to kick on with his career at Trabzonspor.
Elsewhere, West Brom have completed the loan signing of Chelsea sensation Conor Gallagher.
The 20-year-old midfielder has signed a new five-year contract with Chelsea but immediately gone out on loan to the club for the rest of this season.
The gifted Englishman spent the first half of last term on loan at Charlton and the second half at Swansea, winning plenty of admirers for his displays in the Championship.
Aston Villa, Crystal Palace and Leeds United have all been linked with a move for the England youth international, but West Brom have won the hunt to take him on a short-term deal.